Path 2. backdoor path (via a confounder, complexity)
Path 3. backdoor path (via a confounder, complexity)
No direct paths
Multiple closed paths
Biases
Criterion for avoiding biases:
Backdoor criterion: rules to block all (backdoor) paths
those that start with an arrow pointing into the exposue variable (MPA)
Biases
Criterion for avoiding biases:
Backdoor criterion: rules to block all (backdoor) paths that start with an arrow pointing into the exposue variable (MPA)
Frontdoor criterion: rules that enable us to go from the exposure to the outcome via a mediator in a way that avoids backdoors.
Use two paths (mpa -> fishing and then fishing -> biomass).
Multiple coefficients together.
useful when backdoor paths cannot be blocked.
Relation types
X indirectly effects Y through a mediator, M
Conditioning on M blocks the path, resulting in overcontrol bias
Backdoor criterion
not to condition on M
unless we want to estimate the direct effects of X on Y
Relation types
C (confounder) is a common cause of both X and Y
Not conditioning on C results in confounding bias
Conditioning on C blocks the path
Backdoor criterion
to condition on C
Relation types
C (collider) is a common effect of both X and Y
Conditioning on C results in collider bias
X and Y are independent unless we condition on C
Backdoor criterion
not to condition on C
Relation types
acts as a weaker form of either of the other relation types
Biases
Overcontrol bias: is caused when we condition on a mediator thereby blocking the path from the exposure to the outcome.
Confounding bias: is caused when a variable that is a common cause of both the exposure and the outcome (i.e. it is a backdoor path) is not included in a model.
Collider bias: is caused when a variable that is a common effect of the exposure and the outcome (i.e. it is a frontdoor path) is included in a model.
Relation types and biases
what paths are between MPA and fish biomass?
how do we close any backdoors?
Relation types and biases
My brain hurts, this all sounds difficult…
Relation types and biases
R packages dagitty and ggdag
Identify the paths
ggdag_paths(dag, from ="mpa", to ="biomass", text_col ="black") +coord_cartesian(expand =FALSE, xlim=c(0.5, 3.5), ylim=c(0.5,2.5)) +theme_dag_blank(panel.border =element_rect(fill =NA))
Relation types and biases
Path 1 is a pipe
do not condition on fishing
Relation types and biases
Path 1 is a pipe
Path 2 is a fork
do condition on complexity
Relation types and biases
Path 1 is a pipe
Path 2 is a fork
Path 3 is a fork
do condition on complexity
Relation types and biases
Adjustment sets - covariates required to close backdoors